Summary Brief periods of neural activity trigger a vascular response with a complex but fairly stable form. This hemodynamic response function (HRF) is extensively exploited in popular functional imaging methods such as functional magnetic resonance imaging (fMRI) and reflectance based optical imaging. Proper interpretation and utilization of these imaging techniques requires a detailed understanding the HRF. Moreover, because the brain is continually active, transient responses are likely to be important in normal operation of the healthy brain. Cerebrovascular pathology is likely to affect such transient responses, so a more complete understanding of their normal character will enable their use as diagnostics of incipient or extant pathology. The physiology and physics of the HRF are not well understood. The standard ?balloon? model incorporates a non-linear compliant element to explain flow and volume changes. However, the venous volume changes of the balloon model have not been confirmed experimentally, and there is now great controversy on the subject. We have developed a model that combines a novel linear flow description with spatially resolved oxygen transport. The flow model includes the inertial dynamics of moving blood, which cannot be neglected in the larger arterioles that mechanically mediate the flow response. We propose further development of the model, coupled with detailed characterization of the HRF. The model will be expanded to deal with the blood oxygen-level dependent response, and to increase the detail and realism of the flow description. Experimentally, we will use a multi-sensory stimulus protocol with a sensory integration task to evoke the HRF broadly across the brain, and evaluate the responses using high- resolution arterial spin labeling and fMRI to examine the character and variability of these responses within different brain tissues. The results will provide a rich dataset to further test our model and evaluate various hypotheses about neurovascular and neurometabolic coupling.